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A family of pdf's that has been used to approximate the distribution of income, city population size, and size of firms is the Pareto family. The family has two parameters, k and 0, both > 0, and the pdf is as follows. k. gk x20 f(x; k, 0) = + 1 (a) Sketch the graph of f(x; k, 0). f(x) f(x) f(x) f(x) k (b) Verify that the total area under the graph equals 1. dx= (c) If the rv X has pdf f(x; k, 0), for any fixed b > 0, obtain an expression for P(X s b). (d) For 0 < a < b, obtain an expression for the probability P(a sxs b).

A family of pdf's that has been used to approximate the distribution of income, city population size, and size of firms is the Pareto family. The family has two parameters, k and 0, both > 0, and the pdf is as follows. k. gk x20 f(x; k, 0) = + 1 (a) Sketch the graph of f(x; k, 0). f(x) f(x) f(x) f(x) k (b) Verify that the total area under the graph equals 1. dx= (c) If the rv X has pdf f(x; k, 0), for any fixed b > 0, obtain an expression for P(X s b). (d) For 0 < a < b, obtain an expression for the probability P(a sxs b).

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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A family of pdf's that has been used to approximate the distribution of income, city population size, and size of firms is the Pareto family. The family has two parameters, k and 0, both > 0, and the pdf is as follows. gk f(x; k, ө) 3D x < 0 (a) Sketch the graph of f(x; k, 0). f(x) f(x) f(x) f(x) X X X k k (b) Verify that the total area under the graph equals 1. ok dx = + 1 ]: Je x* = 0 - ok =|1 (c) If the rv X has pdf f(x; k, 0), for any fixed b > 0, obtain an expression for P(X < b). (d) For 0 < a < b, obtain an expression for the probability P(a < X < b).
Transcribed Image Text:A family of pdf's that has been used to approximate the distribution of income, city population size, and size of firms is the Pareto family. The family has two parameters, k and 0, both > 0, and the pdf is as follows. gk f(x; k, ө) 3D x < 0 (a) Sketch the graph of f(x; k, 0). f(x) f(x) f(x) f(x) X X X k k (b) Verify that the total area under the graph equals 1. ok dx = + 1 ]: Je x* = 0 - ok =|1 (c) If the rv X has pdf f(x; k, 0), for any fixed b > 0, obtain an expression for P(X < b). (d) For 0 < a < b, obtain an expression for the probability P(a < X < b).
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